\newproblem{lay:3_2_32}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 3.2.32}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Find a formula for $\det\{rA\}$ when $A$ is an $n\times n$ matrix.
}{
   % Solution
	Consider the column decomposition of $A$\\
	\begin{center}
		$A=\begin{pmatrix}\mathbf{a}_1 & \mathbf{a}_2 & ... & \mathbf{a}_n\end{pmatrix}$
	\end{center}
	Then\\
	\begin{center}
		$rA=\begin{pmatrix}r\mathbf{a}_1 & r\mathbf{a}_2 & ... & r\mathbf{a}_n\end{pmatrix}$\\
		$\begin{array}{rcl}\det\{rA\}&=&\left|\begin{array}{cccc}r\mathbf{a}_1 & r\mathbf{a}_2 & ... & r\mathbf{a}_n\end{array}\right|\\
		           &=&r\left|\begin{array}{cccc}\mathbf{a}_1 & r\mathbf{a}_2 & ... & r\mathbf{a}_n\end{array}\right|\\
							 &=&r^2\left|\begin{array}{cccc}\mathbf{a}_1 & \mathbf{a}_2 & ... & r\mathbf{a}_n\end{array}\right|\\
							 &=&r^n\left|\begin{array}{cccc}\mathbf{a}_1 & \mathbf{a}_2 & ... & \mathbf{a}_n\end{array}\right|\\
							 &=&r^n\det\{A\}\end{array}$
	\end{center}
	
}
\useproblem{lay:3_2_32}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
